Orthogonal Matrix

orthogonal matrix

[ȯr′thäg·ən·əl ′mā·triks] (mathematics) A matrix whose inverse and transpose are identical.

Orthogonal Matrix

An orthogonal matrix of order n is a matrix

whose product with the transpose A′ gives the identity matrix, that is, AA′ = E and A′ A = E. The elements of an orthogonal matrix satisfy the relations

or the equivalent relations

The determinant ǀAǀ of an orthogonal matrix is equal to +1 or – 1. The product of two orthogonal matrices is an orthogonal matrix. All orthogonal matrices of order n form, with respect to the operation of multiplication, a group called the orthogonal group. In conversion from one rectangular coordinate system to another, the coefficients a_ij in the coordinate transformation equations

form an orthogonal matrix.

单词	orthogonal matrix
释义	orthogonal matrix orthogonal matrix n (Mathematics) maths a matrix that is the inverse of its transpose so that any two rows or any two columns are orthogonal vectors. Compare symmetric matrix Orthogonal Matrix orthogonal matrix [ȯr′thäg·ən·əl ′mā·triks] (mathematics) A matrix whose inverse and transpose are identical. Orthogonal Matrix An orthogonal matrix of order n is a matrix whose product with the transpose A′ gives the identity matrix, that is, AA′ = E and A′ A = E. The elements of an orthogonal matrix satisfy the relations or the equivalent relations The determinant ǀAǀ of an orthogonal matrix is equal to +1 or – 1. The product of two orthogonal matrices is an orthogonal matrix. All orthogonal matrices of order n form, with respect to the operation of multiplication, a group called the orthogonal group. In conversion from one rectangular coordinate system to another, the coefficients a_ij in the coordinate transformation equations form an orthogonal matrix.
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